Many highly productive oil and gas fields are found in unconsolidated or poorly consolidated rock formations, that is, rock formations in which the individual grains of sand making up the rock formation have not yet become cemented together by the passage of time. Wells in these formations are normally "cased" by lining them with steel pipe. The casing is "perforated" by detonation of an explosive charge or the like within the pipe so as to form orifices in the casing at the depths where it is anticipated that oil and gas will be usefully recovered.
It is well known that in such cases some quantity of the unconsolidated sand tends to flow into the well with the oil and gas. This causes damage to equipment and also necessitates that the sand be removed from the oil or gas which is produced. Furthermore, excessive sand production can cause the entire formation to collapse, necessitating that the well be cleaned out and, in many cases, that it be packed with "gravel", a relatively coarser sand which then acts as a kind of filter. However, such methods are complex and expensive to perform.
The art has realized for some time that when oil and gas are produced from an unconsolidated formation, a so-called "sand arch" can form outside the perforation. When this occurs, sand in the immediate vicinity of the perforation is drawn into the casing, together with the oil and/or gas being produced, leaving a void behind the casing. The void may resemble an arch centered opposite the perforation. The amount of sand flowing into the well is a function of the surface area through which the oil and gas flow. That is, sand is produced when the force exerted due to the viscosity of the oil and gas flowing around the grains of sand is higher than the force holding the formation together, so that the sand tends to flow into the well with the oil and gas.
When a sand arch grows to sufficient size, that is, when a sufficiently large cavity is formed behind the perforation, a metastable condition can result. In this condition, the surface area of the cavity is relatively large compared to the area of the orifice of the perforation. As the cavity grows, the force per unit area exerted on the sand by the flowing oil or gas is reduced until it is equal to the force holding the formation together, so that the structure is relatively stable. However, it will be apparent to those of skill in the art that if the production rate is then increased, as is normally desirable, the sand will tend to be produced and, as noted above, the formation may indeed collapse. It is therefore desirable to produce oil and gas from wells in such unconsolidated or poorly consolidated formations at rates which will not lead to excessive production of the sand and which will allow sand arches, if they form, to be relatively stable.
There is at present no method or apparatus known for determining the size and shape of sand arches. Because they form while the well is being produced, it is difficult if not impossible to generate a meaningful static model. To the knowledge of the present inventors, no method is available in the published art for modeling the formation of sand arches in the laboratory in order to determine the maximum rate at which a well in a particular formation can be produced. It would be desirable to provide an apparatus and technique for laboratory modeling the dynamic production of oil and gas from poorly consolidated formations. In particular, it would be desirable to provide experimental techniques and equipment for monitoring the growth of sand arches, so as to be able to determine for later field use the maximum production rates which are tolerable without excessive production of sand.